Mathematical Physics

1806 Submissions

The Physics of Nothingness

The paper claims that physical laws are amenable to consideration in terms of an algebraic pattern arising solely from the omega constant that underlies both a spatial limit of the universe, implying its scale invariance, and the fine structure constant that stands for changeability of the universe in time. Given that connection, we are able to deduce all fundamental physical quantities exclusively from the omega constant, which makes it possible to meet certain fundamental challenges faced by physics.
Category:Mathematical Physics

Nonlinear Resonances Analysis of a RLC Series Circuit Modeled by a Modified Van der Pol Oscillator

In this paper, the nonlinear resonances analysis of a RLC series circuit modeled by a modified Van der Pol oscillator is investigated. After establishing of a new general class of nonlinear ordinary differential equation, a forced Van der Pol oscillator subjected to an inertial nonlinearity is derived. From this equation the multiple scales method is used to find the various resonant states. As analytical results primary resonance, sub-harmonic resonance of order 1/3 and super-harmonic resonance of order 3 are obtained. The steady-state solutions and theirs stabilities are determined. Numerical simulations display bistability, hysteresis, jump and bifurcation phenomena. The effects of different parameters on the system behavior are investigated and results are presented graphically and discussed.
Category:Mathematical Physics

Present article allowed me to elucidate , the Essence , of what is said for Geometry and Physics . In geometry Point P , is nothing and is possessing Zero-magnitude and Infinite directions. In Material-Geometry , Point is the minimum-energy-cave ,r, in space possessing cave`s ,r, magnitude which is eternally existing from the internal-rotation ≡ motion , of any two Opposites [+ , - ] . Because of this , Material-point is a Quaternion measuring so much the cave`s , r, magnitude as well as the internal eternal-motion which is an oscillatory motion in , n , lobes . In geometry , two Points A,B consist the line-Segment , possessing the |AB| magnitude and AB direction. Euclidean-vector → |AB| , carries Point A to point B , possessing the |AB| magnitude and the two opposite directions → AB , BA ← respectively .
Material-Quaternion or , monad |AB| = z = a + bi , carries motion from Material-point A , to Material point B , where this motion called Work ≡ Spin and is never annihilated .
The non-annihilation of Work ≡ motion , is due to the fact that this happens in the finite –space , r , which is a Stationary-Wave pattern , and thus is the way of Transporting Energy .
In E-Geometry Three Points A , B , P, consist the Plane ABP , i.e. the line AB and point P , not on AB and triangle ABP , which is the Basic-Ideal-Stable-Plane Shape in all states of universe, and for Material triangle is the analogous Regular Hexagon containing all properties of
E-Geometry -triangle multiplied by two .
In E-Geometry Four Points A , B , C , P, consist the Space ABCP , i.e. the Basic-Ideal-Stable and Solid-Shape which is the Tetrahedron , and is the Basic-Element for all structures as Compound-primary particles , Atoms , Molecules , Crystals , etc. N - Points A , B ,,, P,,, P_( N) , consist the Regular-N-Edges shape , ABPP_( N) , i.e. The Regular N - Edges - Polyhedrons , where points , P , P_( N) , do not coincide with the others and consist all Solid Structures.
Any cave , r, containing Opposites Is a Material-Point, and into this cave exists an eternal rotation
of the Positive to the Negative . This motion produces an angular-velocity-vector w, and an angular-momentum-vector , B, and the work produced is equal to 2W = w.B .
Caves r , follow the Euclidean-Geometry of two points Quantization , from point zero which is
nothing or the sum of two equals and opposite , to any number ,n, and to infinite.
The eternal-rotation of Positive to Negative in energy-cave ,r, is proved to be , The eternal-motion which is equal to what is called The Energy from Chaos.
The Spin is proved to be the above rotation on Great or on Small circles in cave , r , on the negative constituent , and is equal to the Angular-momentum-vector B of cave .
Energy-storages is proved to be the n , Stationary and integer-Energy-lobes in cave , r , and which cave r , is a Stationary-wave becoming from the eternal-rotation of opposites.
Photon is proved to be one of the Moving Energy-storages ,[Stationary-Energy-storage-Wave].
Category:Mathematical Physics

On Dirac Negative Mass and Magnetic Monopole

In this work first we discuss the possibility of existence of Dirac negative mass and magnetic monopole by formulating Dirac and Maxwell equations from a symmetrical system of linear first order partial differential equations. Then, by establishing a complete symmetry between space and time, in particular their dual dynamics, we show that the existence of negative mass is the result of dynamical symmetry between space and time, and magnetic monopole is a manifestation of the temporal topological structure of an elementary particle classified by the homotopy group of closed surfaces. We also show that the quantum relationship between the electric charge and the magnetic charge obtained by Dirac can be derived by imposing a topological relationship between the Gaussian curvatures of the temporal and spatial manifolds.
Category:Mathematical Physics

Further Discussions on Geometric Interactions

In this work we discuss further the geometric interactions resulted from the coupling of n-cells that are decomposed from CW complexes. As an illustration, we discuss whether a gravitational field can be considered as the result of a geometric and topological coupling of two decomposed sub-manifolds from CW complexes in terms of Gaussian curvatures of two-dimensional manifolds.
Category:Mathematical Physics

Paths in the Universe

The fact of named one event as unpredictable, is to assume ignorance. Our goal so, is know the evolution of any object or event.
In the nature, there are many events with the same geometry, so is necessary to ask us, if there some think common for all these cases, some law able to means these examples.
That is the main goal for me and this article: know how the nature think and decides, and create language mathematics, pretty and simple, in order to explain any event.
In this article, I explain other vision of economy for example, and its evolution and also the relation between human feelings and the cosmos evolution through paths or ways. I love the knowledge and know the future based in the past.
Category:Mathematical Physics

An Intuitive Approach to the Coherent and Squeezed States of the Quantum Harmonic Oscillator

The purpose of this work is to introduce, in a simple, intuitive way, the coherent and squeezed states of the quantum harmonic oscillator (QHO), through a series of exercises, which are solved in detail.
Starting from the application of a spatial translation to the ground state of the QHO, we introduce the spatial and momentum translations, focusing on their application to the QHO, which leads us to the displacement operator.
Next, we introduce the coherent states and examine their basic aspects.
We then proceed to give a simple and purely intuitive introduction to the squeezed states and we conclude by identifying the coherent states as states of minimum energy expectation value compared to the respective squeezed states.
The reader is assumed to have a basic knowledge of the postulates and the mathematical formalism of quantum mechanics, including the Dirac notation and the ladder operator method of the QHO.
Category:Mathematical Physics

First Newtonian Analyzes of the Michelson-Morley Experiment Using the Fixed Elastic Collision Law

In these papers, physicists will find the latest mathematical analysis of the results of the Michelson-Morley experiment, which was the source of all papers for Fitzgerald, Lorentz, Poincare, Minkowski and Einstein. This analyzes are the result of a study of the elastic collision theory, and are quite different from those of early physicists who have paved the way for the emergence of relativity theory. This work will discuss Fitzgerald-Lorentz's explanations and prove that they are not correct.
Category:Mathematical Physics